Authors: Nathan O. Schmidt
Our objective is to design and formulate an abstract, easy-to-visualize, and flexible geometric information structure in a 4D space-time with direct application to mathematics and physics. For this, we introduce and define the "Riemann tesseract": a 4-cube of dual interconnected 3-cubes which are inferred from a topological Riemannian circle that is isometrically embedded in a 1D Riemann surface. The Riemannian circle is a 2-sphere, stereographic superlense, Gedanken interferometer, and double-negative index meta-material that may be scaled to any size, and serves as a common 2D surface boundary between dual interconnected 3-branes: it is a time-like region that is simultaneously dual to both "micro" and "macro" space-like regions. From scratch, we geometrically and topologically construct the information structure in a generalized coordinate system that is compatible with the Schwarzschild metric. Complex order parameter fields are assigned to the tesseract's vertices to systematically encode its wavefunction state space using a relatively simplistic methodology. The number of distinct order parameter fields at each vertex is variable and is application-dependent; it is trivial to vary the complexity of the system by adding or subtracting representational degrees of freedom because the "core" tesseract structure remains unchanged. We mathematically prove that this general and configurable model is consistent with the CPT-theorem, and is fully-capable of representing the simultaneous breaking of multiple symmetries.
Comments: 8 pages and 2 figures
[v1] 2012-10-21 23:03:55
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